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Mathematical analysis of an age structured heroin-cocaine epidemic model

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This paper is devoted to studying the dynamics of a certain age structured heroin-cocaine epidemic model. More precisely, this model takes into account the following unknown variables: susceptible individuals, heroin users, cocaine users and recovered individuals. Each one of these classes can change or interact with others. In this paper, firstly, we give some results on the existence, uniqueness and positivity of solutions. Finally, some numerical simulations are presented to illustrate our theoretical results. Figure 1. Transfer diagram for model 1. Figure 2. Figure 3. Figure 4. Figure 5. Figure 6. Table 1. Description of each symbol in model 1. Figures 6. Tables 1. Article Contents. Doi: This issue Previous Article Kink solitary solutions to a hepatitis C evolution model Next Article Spreading speeds for a class of non-local convolution differential equation. Mathematical analysis of an age structured heroin-cocaine epidemic model. Received: December Download: Full-size image PowerPoint slide. Show Table. DownLoad: CSV. Related Papers. Cited by. Bai and S. Zhang , Traveling waves of a diffusive SIR epidemic model with a class of nonlinear incidence rates and distributed delay, Commun. Nonlinear Sci. Berman and R. Burattini , E. Massad , F. Coutinho , R. Azevedo-Neto , R. Menezes and L. Chekroun , M. Frioui , T. Kuniya and T. Touaoula , Global stability of an age-structured epidemic model with general Lyapunov functional, Math. Diekmann and J. Heesterbeek, Mathematical Epidemiology of Infectious Diseases. Djilali , T. Touaoula and S. Miri , A heroin epidemic model: Very general non linear incidence, treat-age, and global stability, Acta Appl. Ducrot and P. Magal , Travelling wave solutions for an infection-age structured model with diffusion, Proc. Edinburgh Sect. A , , Fang , X. Martcheva and L. Cai , Global stability for a heroin model with two distributed delays, Discrete Contin. B , 19 , Cai , Global stability for a heroin model with age-dependent susceptibility, J. Cai , Global asymptotic properties of a heroin epidemic model with treat-age, Appl. Hosono and B. Ilyas , Traveling waves for a simple diffusive epidemic model, Math. Models Methods Appl. Huang and A. Liu , A note on global stability for a heroin epidemic model with distributed delay, Appl. Kermack and A. McKendrick , A contribution to the mathematical theory of epidemics, Proc. Lin , C. Ma and F. Liu and X. Liu , Mathematical analysis for an age-structured heroin epidemic model, Acta Appl. Liu and T. Zhang , Global behaviour of a heroin epidemic model with distributed delays, Appl. Liu , X. Liu and J. Wang , Threshold dynamics of a delayed multigroup heroin epidemic model in heterogeneous populations, Discrete Contin. B , 21 , Wang , Epidemic dynamics on a delayed multi-group heroin epidemic model with nonlinear incidence rate, J. Magal, Compact attractors for time-periodic age-structured population models, Electron. Differential Equations , , 35pp. McCluskey , Global stability for an SEI epidemiological model with continuous age-structure in the exposed and infectious classes, Math. Mulone and B. Straughan , A note on heroin epidemics, Math. Samanta , Dynamic behaviour for a nonautonomous heroin epidemic model with time delay, J. Smith and H. Thieme and C. Thieme , Semiflows generated by Lipschitz perturbations of non-densely defined operators, Differential Integral Equations , 3 , Wang and X. Wang and J. Wu , Travelling waves of a diffusive Kermack-McKendrick epidemic model with non-local delayed transmission, Proc. A Math. Weng and X. Differential Equations , , White and C. Xu , Traveling waves in a Kermack-Mckendrick epidemic model with diffusion and latent period, Nonlinear Anal. Yang, X. Li and F. Zhang, Global dynamics of a heroin epidemic model with age structure and nonlinear incidence, Int. Zhang , B. Li and J. Shang , Stability and travelling waves for a time-delayed population system with stage structure, Nonlinear Anal. Real World Appl. Access History. Figures 6 Tables 1. Export Citation. Citation Only. Citation and Abstract. Export Close.

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